Open Research Index

BKARForestFormula

Scott Armstrong

Palomar Registrypalomar/PALOMAR-2026-09-19-000003Sep 19, 2026math-phscore 0

A Lean 4 / Mathlib formalization of the Brydges-Kennedy-Abdesselam-Rivasseau forest interpolation formula: for a finite vertex set V and a C-infinity function rho on the edge-coupling space of the complete graph on V, the value of rho at the all-ones coupling equals the sum, over all acyclic edge subsets (forests) F, of the integral over the unit cube [0,1]^E(F) of the mixed partial derivative of rho in the edge variables of F, evaluated at the path-minimum interpolation point x^F(u); the empty forest contributes rho(0). The flagship theorem is additionally restated Mathlib-only and…

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